The Verification Method of MASOES applied to the Social Force Model for Pedestrian Dynamics

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1 The Verfcaon Mehod of MASOES appled o he Socal Force Model for Pedesran Dynamcs NIRIASKA PEROZO 1, JOSE AGUILAR 2, OSWALDO TERÁN 2,3 1 Undad de Inelgenca Arfcal, Decanao de Cencas y Tecnología, Unversdad Cenroccdenal Lsandro Alvarado, Barqusmeo 31, VENEZUELA. 2 CEMISID, Faculad de Ingenería. Unversdad de los Andes, Mérda 511, VENEZUELA. 3 CESIMO, Faculad de Ingenería. Unversdad de los Andes, Mérda 511, VENEZUELA. nperozo@ucla.edu.ve, agular@ula.ve, oeran@ula.ve Absrac: - MASOES s a mulagen archecure for desgnng and modelng self-organzng and emergen sysems. The archecure descrbes he elemens, relaonshps and mechansms, boh a he ndvdual and he collecve levels, whch deermne he self-organzng and emergen phenomena, whou mahemacally modelng he sysem. In hs work s esed a mehod of verfcaon for MASOES, n order o deermne s qualy o descrbe he self-organzng and emergen behavor of real sysems. Ths mehod s based on he wsdom of crowd paradgm and fuzzy cognve maps. The case sudy s based on socal force model for pedesran dynamcs, n order o sudy s behavor and deermne s self-organzng and emergen capacy hrough MASOES. Key-Words: - Mulagen sysems, Self-Organzaon, Emergen Sysems, Socal Force Model, Crowd Dynamcs. 1 Inroducon Nowadays, he mulagen approach can be used o model sysems wh several agens and neracons n very dynamc and/or unpredcable envronmens, where soluons are no known beforehand, and/or change consanly. Thus, we defne MASOES, a mulagen archecure for desgnng, modelng and sudyng self-organzng and emergen sysems [1], whou mahemacally modelng he sysem. MASOES, wh respec o oher works [7, 11 and 14], consders boh mcroscopc and macroscopc aspecs of a sysem; ha s, manages he knowledge a he collecve and ndvdual level. Also, s a generc archecure and allows each agen o change s behavor, guded by s emoonal saes, provdng o he sysems desgner wh a ool ha can be appled n he modelng of self-organzng and emergen sysems n dfferen conexs. In hs paper, he case sudy s appled o he Socal Force Model (SFM) [8], whch s a mcro-smulaon model for sudyng pedesran dynamcs, hrough dverse forces for reflecng he movaons of he pedesran and he nfluence of envronmen. Hence, hs arcle esablshes he archecural componens of MASOES and he causng relaonshps beween hem for he SFM. Tha s, for hs specfc case where we know ha he real sysem (SFM) has selforganzng and/or emergen properes, we are gong o es f he verfcaon mehod of MASOES can deermne s self-organzng and/or emergen properes, as hose are observed n real expermens [9, 1]. 2 General Aspecs Ths secon defnes some aspecs relaed o MASOES, he wsdom of crowds paradgm (WoCP), he fuzzy cognve maps (FCM), and fnally, abou SFM. 2.1 MASOES MASOES s a mulagen archecure for sudyng sysems n order o deermne her self-organzng and emergen properes. We shall descrbe some key ISBN:

2 aspecs n a general way (more deals abou componens and mechansm can be found n [1]). Our archecure s dvded no wo levels: ndvdual and collecve (see fgure 1). Collecve cognve emergence arses from hree neracon levels: Local Ineracon Level, whch mgh be drec or ndrec (va he envronmen); Group Ineracon Level, nvolvng socal neworks or srucured groups; and, General Ineracon Level, whch ncludes he whole he communy of agens. Now, wh respec o ndvdual cognve emergence, he dea s o produce cognve emergence mang he way n whch human beng go from unconscous o conscous; handlng he agen s behavor a 3 dfferen levels and esablshng a herarchy of behavors: Unconscous Behavor or reacve; Emoonal Behavor orened by he emoons; and Conscous Behavor. Each agen changes s behavor (behavor-swchng) dynamcally, guded by s emoonal sae n a gven momen. We propose n [2], an emoonal model whch wll be used as an ndrec mechansm n he decson-makng process and n choosng ype of behavor n parcular. Fg. 1. Mulagen Archecure for Self-Organzng and Emergen Sysems. 2.2 Wsdom of Crowds Paradgm Accordng o hs paradgm, he collecve nellgence (global wsdom) emerges from he knowledge of ndvduals whn a group where evenually each separae ndvdual possesses lle nformaon. In pracce, he concep of collecve nellgence s he oppose of he so-called exper opnon, whch means consulng wh a person ha has a rack record of good judgmen based on her experence and specalzed knowledge [2]. Ths s proven hrough dfferen examples where can be seen how he aggregaed knowledge of a large and dverse group s superor o ha of one or few expers. Accordng o Suroweck [2], here are some wsdom of crowd prncples ha we use as a source of nspraon n order o defne our verfcaon crera n [12]. These prncples are: Opnon Dversy: Indvduals mus have suffcenly dverse opnons (or knowledge over an ssue) as o be able o comprse he whole specrum of possble opnons. Wh more dversy n a crowd more robus wll be her collecve nellgence. Independence of Opnon: Each person mus feel ruly free o express hs opnon, whou beng nfluenced by ohers, ha s, as auonomously as possble. Decenralzaon: Decenralzaon means ha each person pus hs pon of vew o he es, nsead of smply answerng o drecves comng from above,.e., each member ac as a pseudo-exper of an area. Aggregaon: There are a decenralzed and dsrbued mechansm ha summarzes, ransforms and expresses ndvdual conrbuons (ndvdual knowledge) no collecve conrbuons (group knowledge). 2.3 Fuzzy Cognve Maps (FCM) Cognve maps are ools o represen complex cognve process hrough a vsual desgn n he form of a map. Polcal scens Axelrod (1976) [5, 6] nroduced cognve maps as ools o represen socal scenfc knowledge. Cognve maps may be graphcally represened, where conceps are conneced by arrows or hrough a connecon marx n whch he neracon of each par of conceps ndcaes he relaonshp beween hem. In he connecon marx he -nh lne represens he wegh of he arc connecons whch are dreced ousde of he C concep, ha s, hose affeced by C. The -nh column lss he arcs dreced owards C, ha s, hose affecng C. Thus: w, j M C, C j (1) Where M represens he causal funcon of he arc ha has concep C as he precedng concep and C j as he consequen concep, and where w,j wll be he wegh of he relaonshp beween hese wo conceps. In general, concep C ncreases C j causally f w,j = 1, decreases causally f w,j = -1, and has no a causaly relaonshp f w,j =. Wh respec o he FCMs, hese were developed by Kosko [4] n he md-198s from Axelrod s Cognve Maps. FCMs were nally presened as fuzzy mechansms, where conceps and relaonshps could be represened as fuzzy varables (expressed n lngusc erms). In a FCM he level of represenaon of each concep depends on he level of s anecedens n he prevous eraon, and s calculaed hrough a normalzed sum of producs, where he relaonshp beween a concep and s anecedens s modeled by a smple wegh, accordng o he followng equaon: ISBN:

3 C m 1 S k N 1 w m, k (2) Where C m (+1) ndcaes he value of he concep n he followng eraon, N ndcaes he number of conceps, w m,k ndcaes he value of he causal relaonshp beween he concep C k and he concep C m and S(y) s a funcon o normalze he value of he concep. Fnally, he dynamc approach of he FCM (Dynamc Fuzzy Cognve Maps, DFCM) [17] s based on he dynamcs of he causal relaonshps,.e. durng he runme adap o he changes arsng n he envronmen. 2.4 Descrpon of he MASOES Verfcaon Mehod For he MASOES verfcaon s used wo ypes of conceps (more deals can be found n [12]): Archeconc Conceps: These are he conceps lnked o he collecve and ndvdual componens proposed n MASOES, such as: agens, drec and ndrec neracons, learnng, posve and negave feedback, aggregaon mechansms, among ohers. Conceps lnked o self-organzng and emergen properes: These are he conceps lnked o he verfcaon crera ha guaranee emergence and self-organzaon n a complex sysem: densy, dversy, ndependence, emoveness, selforganzaon and emergence. These conceps, once hey have been nsanced n an applcaon, should ensure he exsence of ceran self-organzng and emergen phenomena such as: qualy conen, group formaon, generaon of rules, among ohers Inalzaon Phase of Verfcaon Mehod Here s assgned a wegh o each relaonshp among conceps accordng o expers. The relaonshps are esablshed usng an adjusmen funcon based on fuzzy rules defned n [5, 12]. Moreover, s assumed ha he sae of he conceps n a modeled sysem can be locaed n hree zones: low, medum and hgh [5]. A concep has a hgh sae (beween 2/3 and 1) when works correcly and conrbues subsanally wh he funconng of he modeled sysem. A concep has a medum sae (beween 1/3 and 2/3) when s funconng mus be valdaed and s conrbuons o he sysems funconng s no so subsanal. A concep has a low sae (beween and 1/3) when does no work and does no conrbue o he funconng of he sysem Execuon Phase of Verfcaon Mehod The execuon algorhm, accordng o he specfed adjusmen funcon, s he followng: C k I. To oban he nal saes for all he conceps accordng o he sysem o model and o he scenaro C c c c o evaluae, 1,..., n. II. Whle he sysem does no converge o a seady sae: a. To oban he values of he causal relaonshps w hrough, j df, j C 1 df j, where, s he adjusmen w, j. funcon for he relaonshp b. To oban he curren saes n c j w, j c hrough. III. Inerpreaon of he Resuls. Fg. 2. The Generc FCM for our verfcaon mehod. 1 Ths algorhm s done hrough a ool called FCM Desgner, ool creaed n Java o vsually creae and o execue a FCM or DFCM (more deals n [5]). Thus, he Generc FCM (see fgure 2) s desgned and negraed wh he values assgned o each one of he relaonshps defned by he expers. In summary, he nsanaon of he verfcaon mehod for a sysem modeled hrough MASOES consss of defnng he possble scenaros and hen, o nalze he conceps accordng o he characerscs and operaon of he sysem o sudy for a gven scenaro (sep I of he algorhm). Laer, accordng o sep II, we would have a FCM of he modeled sysem ha we mus erae wh he FCM Desgner, unl he sysem becomes sablzed. Fnally, we make he analyss and nerpreaon of he resuls. 2.5 Socal Force Model In he followng, he man effecs accordng o SFM [8] ha deermne he moon of a pedesran, wll be nroduced: ISBN:

4 () Drvng Force. He/She wans o reach a ceran r desnaon as comforable as possble. Therefore, he/she normally akes he shores possble way. Hs/her desred drecon e of moon wll be: k r r e :, k r r (3) Where r denoes he acual poson of pedesran a me. And, he/she wll a every me seer r for he neares pon k. If a pedesran s moon s no dsurbed, he/she wll walk no he desred e drecon wh a ceran desred speed. A devaon of he acual velocy from he desred : e velocy due o necessary deceleraon processes, or avodance processes, leads o a endency o approach agan whn a ceran relaxaon me. Ths can be descrbed by an acceleraon erm of he form: 1 F, e : e. (4) () Repulsve Effecs. The moon of a pedesran s nfluenced by oher pedesrans. In parcular, he/she keeps a ceran dsance from oher pedesrans ha depends on he pedesran densy and he desred speed. Ths resuls n repulsve effecs of oher pedesrans ha can be represened by vecoral quanes: F r : r V b r (5) V b We wll assume ha he repulsve poenal s a monoonc decreasng funcon of b wh equpoenal lnes, havng he form of an ellpse ha s dreced no he drecon of moon. Where r s he order of he sep wdh of pedesran. A pedesran also keeps a ceran dsance from borders of buldngs, walls, srees and obsacles, among ohers. Therefore, a border B evokes a repulsve effec ha can be descrbed by: F B r B : r U B r B B (6) Wh a repulsve and monoonc decreasng U B r B r poenal. Where B denoes he locaon of ha pece of border B ha s neares o pedesran. () Aracve Effecs. Pedesrans are somemes araced by oher persons (e.g. frends, sree arss, ec.) or objecs (e.g. wndow dsplays, ec.). These F aracve effecs a places r can be modeled by aracve, monoonc ncreasng poenals W r, n a smlar way lke he repulsve effecs: F r, : r W r, (7) F The man dfference s ha he aracveness s normally decreasng wh me snce he neres s declnng. We can now se up he equaon for a F pedesran s oal movaon. The oal SFM s [8]: F : F, e F e, r r F B e, r rb F e, r r,. B (8) The socal force model s now defned by: dw : F flucuaons. d (9) Where w s he preferred velocy. Here we have added a flucuaon erm ha akes no accoun random varaons of he behavor. Ths flucuaon s Gaussan dsrbued and perpendcular o he vecor ponng n he desred drecon. In order o complee he model of pedesran dynamcs, a relaon beween he acual velocy and he preferred velocy w mus be nroduced for he nex movemen. 3 Case Sudy: Socal Force Model In hs case we wll characerze he ndvdual and collecve levels of he componens and processes nvolved n he SFM [8] va MASOES. Laer, hs wll allow us o evaluae f he SFM behaves as a selforganzng and emergen sysem accordng o he model generaed by MASOES, usng he verfcaon mehod descrbed n [12]. A. SFM accordng o MASOES. In hs secon, SFM s descrbed usng MASOES, followng he mehodology proposed n [13]. The frs hree sages: analyss, desgn and negraon are descrbed n hs secon. I) Analyss Sage: I.1. Agens and her Tasks n SFM Modelng SFM hrough MASOES means o consder he pedesrans as agens wh a hgh degree of homogeney,.e., wh a large quany of pedesrans ISBN:

5 wh a smlar behavor. Pedesrans nerac n a common space, he sree (envronmen), and each pedesran obeys he same se of rules or forces defned n [8] and descrbed n secon 2.5, n order o reach hs/her objecve (desnaon). I.2. Ineracon Levels There are 3 levels of neracon: Local. Pedesrans nerac wh each oher n a drec and ndrec manner when each pedesran mus selec he drecon and speed n relaon o oher pedesrans, obsacles, ec. n order o produce hs/her local moon. Moreover, each pedesran acs n agreemen wh he local nformaon and hs/her objecve, avodng borders and oher pedesrans. Group. In hs level, he pedesrans should nerac followng he aracve and repulsve effecs whch are responsble for he formaon of pedesran groups (jonng behavor). General. I represens he hghes neracon level, where he neracons are among he exsng flows of pedesrans (crowd moon). II) Desgn Sage: II.1. SFM s Componens and Processes a he Indvdual Level In hs secon, he SFM s componens and processes a he ndvdual level are descrbed. Accordng o he SFM, he pedesrans mus be defned whou emoons because hey are no consdered n he SFM. Addonally, s convenen ha he agens develop wo ypes of behavor proposed by MASOES (reacve and mave) n accordance wh SFM equaons. Thus, each pedesran agen wll have he 3 ndvdual componens: reacve, socal and behavor componen n MASOES, whou he cognve componen (see able 1). II.2. SFM s Componens and Processes a Collecve Level The nvolved componens and processes can be seen n ables 2 and 3, respecvely. III) Inegraon Sage: III.1. Phases for Knowledge General Managemen n he SFM In he able 4, he hree phases of our archecure for he knowledge managemen are nsanced for he SFM. In spe of he fac ha here s neher a collecve objecve nor a collecve knowledge base, and nor an emoonal or cognve behavor, accordng o he nsanaon of he analyss, desgn and negraon sages n he SFM, can be affrmed, n accordance wh MASOES, ha he modeled sysem has he key componens and processes, a he ndvdual and Table 1 Indvdual Componens of MASOES n SFM INDIVIDUAL REPRESENTATION IN THE SFM COMPONENT IN MASOES The pedesrans n he SFM acvae her Behavor behavor dependng on he suaon hey face a a gven me. The equaons of he SFM descrbe dfferen forces whch wll allow he behavoral componen o dynamcally carry ou changes of he agen s behavor. Reacve Pedesrans demonsrae reacve behavor n case of avodng collson wh oher pedesrans or obsacles, and for mananng a segregaon behavor n case of walkng n group or beng araced by somehng or some person. Cognve I s no represened by he SFM for pedesran dynamcs. Each pedesran requres space for he nex Socal sep, whch s aken no accoun by oher pedesrans. Hence, he behavor of each pedesran depends on he poson and velocy of he oher pedesrans and he envronmen, n order o adjus hs/her velocy. Table 2 MASOES Collecve Componens n SFM COMPONENT REPRESENTATION IN SFM IN MASOES Se of Rules Ths se of rules s made up of all he equaons of he SFM. I s hanks o he se of drec and ndrec Acon Feld neracons ha he pedesrans delm her acon feld whn he pedesran envronmen (he sree). In fac, hs acon feld s made up of he pedesrans s rajecores. Collecve There s no a collecve knowledge base n Knowledge Base he SFM. Collecve There s no a collecve objecve n he Objecve SFM. Table 3 MASOES Collecve Componens n SFM COLLECTIVE PROCESSES Formaon of Socal Neworks Feedback Mechansms REPRESENTATION IN SFM We shall consder a socal nework as an open, horzonal sysem, groupng a number of people denfed wh smlar needs and problems and whch, addonally, work ogeher wh nense socal neracon n order o maxmze resources and conrbue o he soluon of problems [4]. Socal neracon for problems resoluon n he SFM does no ake place snce each pedesran has only hs/her objecves whou a collecve or common objecve. Wh respec o flows generaon, here are mechansms for he generaon of pedesrans s rajecores. The nvolved feedback mechansms n he SFM are: Acceleraon Process guded by acual velocy, desred speed. Deceleraon or Avodance Processes such as: repulsve and aracon effecs. ISBN:

6 Table 4 SFM hrough he Knowledge Managemen Phases PHASE REPRESENTATION IN THE SFM Socalzaon Pedesrans make explc her knowledge o he ohers hrough creaon, modfcaon and elmnaon of hs/her rajecory. The aggregaon process s carred ou hrough Aggregaon he poenal felds formed by he dfferen forces from all he pedesrans who nerac n he envronmen (sree). Thus, he aggregaon of he movemens of he pedesrans forms dfferen rajecores ha are ranslaed n flows a macro level. Pedesrans could nerac or o communcae wh oher pedesrans drecly or ndrecly, Appropraon bu SFM consders he pedesrans lke unhnkng elemens. For hs, pedesrans have no an explc learnng mechansm n hs model. However, here s a renforcemen learnng lke n he case of he colones of ans, snce he pedesrans can follow or no oher pedesrans (aracon or repulson effecs). Table 5 Defnon of he conceps lnked o he self-organzng and emergen properes n SFM Concep Descrpon Densy Dversy Gaherng Independenc e Emoveness Selforganzaon Emergence I measures he degree of complexy whn he socey of agens. I s measured hrough he number of agens as well as he drec and ndrec neracons. In he SFM s necessary a hgh densy of pedesrans so ha he self-organzaon effecs can happen [9]. I measures he homogeney or heerogeney of he socey of agens. For he SFM here are a number of agens of same ype defned whn he sysem,.e. There s a hgh homogeney. I measures he degree of aggregaon n he sysem, measured by he qualy of he aggregaon mechansm, he feedback mechansms used n he sysem, and he degree of delmaon of he acon feld ha favor coordnaon of acves a a collecve level. I measures he degree of auonomy and appropraon of he agens. Agens should be capable of ssung her own opnons ndependenly, ha s, whou he nfluence and manpulaon of ohers. I s measured by he qualy of he learnng mechansm used by he agen, and by he decsons hey make whou mang ohers, based on her cognve and reacve behavor and on he use of ndvdual emoons, more han he socal ones. I measures he degree of emoveness n he agen. Wh respec o SFM, he handlng of emoons n s mahemacal model s no consdered. I measures he degree of adapably n a sysem. Hence, he spaoemporal paerns (self-organzed phenomena) whch could emerge are he resul of a self-organzaon process among pedesrans raher han of exernal forces or delberave acons [3, 9]. I measures he degree of sysem s evoluon hrough he possbly of he appearance of emergng properes. In pedesran crowds are spaoemporal paerns ha could emerge such as: he developmen of lanes (groups) conssng of pedesrans walkng n he same drecon. Oscllaory changng of walkng drecon a narrow passages (e.g. Doors) and, sponaneous formaons of roundabou raffc a nersecons,.e., he behavoral paerns are cluserng, lanes and queues. collecve levels, n order o generae self-organzng Table 6 Defnon of archeconc conceps of Level II n SFM Concep Descrpon Agen N Agen Behavor Type Drec Ineracon Indrec Ineracon Feedback Mechansm + Feedback Mechansm. - Aggregaon Mechansm I refers o he number of pedesrans n he sysem. I refers o he dfferen ypes of behavor he agens mgh have. In SFM, here are homogeneous agens n he sysem wh a reacve and mave behavor. I refers o he number of neracons beween he pedesrans n he sysem, for example, collsons and oral communcaon. I refers o he number of neracons beween he pedesrans n he sysem hrough he envronmen, for example, he generaed rajecores n he sree hrough her seps. I refers o how correcly he mechansm works. In case of SFM s represened hrough he acceleraon force, whch s a renforcng mechansm ha affecs he aggregaon process, conrbues o mave or socal behavor and acs locally [15, 16]. I refers o how correcly he mechansm works. In case of SFM s represened hrough he deceleraon process, whch s a mechansm o sablze processes and selfregulae hem, avodng undesrable flucuaons. I leads o adapve, emergng behavor, favors robusness before new suaons and acs globally [15, 16]. I represens he qualy of he mechansm n charge of obanng nformaon relave o each ndvdual and combnng n such a way ha may be useful o he collecve. In he SFM, lke a sgmergc sysem, s a decenralzed and dsrbued aggregaon mechansm ha allows ndrec coordnaon and communcaon hrough acon felds or poenal felds. and emergen behavors a he macro level lke a sgmergc sysem, wh a reacve and mave behavor guded by responses, n an envronmen wh an acon feld as aggregaon mechansm. Besdes, he modeled sysem has a hgh densy of pedesrans and behavors based on he local neracons. B. SFM hrough MASOES S Verfcaon Mehod. In hs secon are nsanaed he archeconc conceps and he conceps lnked o self-organzng and emergen properes for he SFM accordng o he sages descrbed n prevous secon, see ables 5, 6 and 7. 4 Expermens Scenaro 1: SFM hrough MASOES. For he nsanaon of SFM hrough MASOES, he nal values of he archeconc conceps were deermned accordng o he used values for he key parameers n ISBN:

7 Table 7 Defnon of archeconc conceps of he level III n SFM CONCEPT Reacve Componen Cognve Componen Behavoral Componen Socal Componen Type of Emoon DESCRIPTION I represens he qualy of hs componen for producng reacve behavor n he pedesran. Reacons are rules assocaed o walkng, obsacle and pedesran collson avodance and aracve effecs. I represens he qualy of hs componen for producng cognve behavor hrough he cognve mechansms (learnng, reasonng) of he pedesran, and also of nenonal or delberae decson-makng, among ohers. In he SFM, hs componen s no represened. I represens he qualy of hs componen for favorng he adapaon of each pedesran wh s envronmen, snce creaes an nernal model of he world (handlng explc knowledge) ha regulaes s behavor. In he SFM, he pedesran has hs/her decson-makng process based on s ndvdual goals snce an emoonal sae s no consdered. I represens he qualy of hs componen for promong conscousness n pedesrans abou he poson and speed of ohers pedesrans. I refers o he ype of emoon an agen mgh have a any gven me. In he SFM, emoons are no consdered n pedesrans. he smulaons done recenly wh hs model [9, 18]. The values of he conceps lnked o he selforganzng and emergen properes are nalzed n zero n order o deermne whch values wll be reached when he sysem s sablzed. In addon, he ype of emoon and cognve componen conceps are nalzed n zero also, snce here s neher emoonal nor cognve managemen n he SFM s pedesrans. Fnally, a hgh densy of pedesrans s assumed accordng o [9], as well as he number of ndrec neracons, snce he pedesrans communcae more ndrecly han drecly [19] followng he seps of oher pedesrans. Therefore, he number of agens and ndrec neracons conceps are nalzed a 1, and drec neracons concep a.25. The oher conceps of he verfcaon mehod ha represen he qualy of he nvolved mechansms assume ha work correcly, for hs reason, hese conceps are nalzed a 1 (see fgure 3). Accordng o he obaned resuls for hs scenaro (see fgure 4), was reached a medum level of selforganzaon (41%) and emergence (43%), verfyng wh hese resuls ha he SFM s a model able o generae self-organzaon and emergence. The conceps emoveness, agen behavor ype, dversy and ndependence fnshed n values close o zero, snce he pedesrans do no have emoons, nor cognve behavor, nor dversy (hgh homogeney) nor ndependence (auonomy). The qualy of he socal componen (1.) s hgher han he qualy of Fg. 3. Scenaro 1: Inal FCM for he SFM. he reacve componen (.69), hs could be because each pedesran has an mave behavor more han reacve owards he end, ndcang ha each pedesran has adaped hs/her behavor o he envronmen and he oher pedesrans when he sysem s sablzed. Accordng o [19], hs mave behavor predomnaes when he sysem selforganzes. Fg. 4. Obaned Resuls for Scenaro 1. On he oher hand, densy reaches (.82) owards a he end snce ndrec neracons decrease of 1 o.86 bu hey connue hgher han he drec neracons (Zero). The decrease n he number of drec neracons are explaned hrough segregaon effec of lane formaon [9], normally leads a he end o a more effecve pedesran flow snce meconsumng avodance maneuvers occur less frequenly.e., s reduced he number of encouners wh opposely movng pedesrans. The slgh decrease n he number of ndrec neracons s due o a predomnanly mave behavor raher han reacve a he end. The concep agen behavor ype n zero explans he hgh homogeney of he pedesrans accordng o he SFM. Besdes, all he oher conceps reach a hgh sae ndcang ha hey ISBN:

8 work properly and conrbue sgnfcanly o he level of self-organzaon and emergence obaned. 5 Concluson The neres of hs sudy was o es he verfcaon mehod n a sysem formally modeled, and found ha performs well.e. s able o deec he selforganzng and emergen properes of he sysem. Thereby, MASOES s showed as an neresng ool for modelng sysems wh or whou known selforganzng and emergen properes and for sudyng he self-organzng and emergen behavor of he modeled sysem. The case sudy based on he SFM s useful o valdae he verfcaon mehod for MASOES, snce allows showng s capably o predc/sudy self-organzng and emergen behavors n real sysems. In prevous works were modeled hrough MASOES oher applcaons, such as Wkpeda and Free Sofware Developmen [12, 13] (boh collaborave and parcpave archecures), hs work s n an aemp o capure he characerscs and properes of anoher ype of sysem, wh a known self-organzng and emergen behavor lke SFM, whch has a wellknown mahemacal model o descrbe how he pedesrans organze hemselves no counerflowng sreams n a corrdor. References: [1] Perozo, N., Agular, J., Terán, O. Proposal for a Mulagen Archecure for Self-Organzng Sysems (MA-SOS). Lecure Noes n Compuer Scence Vol. 575, 28, pp [2] Suroweck, J. Wsdom of Crowds. New York: Random House, 25. [3] Schwezer, F. Brownan Agens and Acve Parcles - Collecve Dynamcs n he Naural and Socal Scences. Sprnger-Verlag, 23. [5] Agular J., Conreras, J. The FCM Desgner Tool. Fuzzy Cognve Maps: Advances n Theory, Mehodologes, Tools and Applcaons, Ed. Glkas Mxals, 21, pp [6] Axelrod, R. Srucure of Decson: The Cognve Maps of polcal Eles. Prnceon Unv. Press, Prnceon, NJ, [7] Gershenson, C. Towards a General Mehodology for Desgnng Self-Organzng Sysems. In Bogg, J. and R. Geyer (eds.) Complexy, Scence and Socey. Radclffe Publshng, Oxford 27. [8] Helbng D., Molnar P, Socal force model for pedesran dynamcs. Physcal Revew E, 1995, 51: [9] Helbng D. e al. Self-Organzed Pedesran Crowd Dynamcs: Expermens, Smulaons, and Desgn Soluons. Transporaon Scence.Vol. 39, No. 1, 25, pp [1]Couzn I., Krause J. Self-organzaon and collecve behavor n verebraes. Advances n he Sudy of Behavor, 23, 32: [11]Zambonell, F., Omcn, A. Challenges and Research Drecons n Agen-Orened Sofware Engneerng. Auonomous Agens and Mul-Agen Sysems, 24, pp [12]Perozo, N., Agular, J., Terán, O., Molna, H., A Verfcaon Mehod for MASOES. Submed for Publcaon o IEEE Transacons on Sysems, Man, and Cybernecs, Par B: Cybernecs, 21. [13]Perozo, N., Agular, J., Terán, O., Molna, H., Self-organzaon and Emergence phenomena n Wkpeda and Free Sofware Developmen usng MASOES. Submed for Publcaon o Cybernecs and Sysems an Inernaconal Journal, 21. [14]Wolf, T., and Holvoe, T., Towards a Mehodology for Engneerng Self-Organsng Emergen Sysems, SOAS, 25 pp [15]Ramos, V., e al. Socal Cognve Maps, Swarm Collecve Percepon and Dsrbued Search on Dynamc Landscapes. Journal of New Meda n Neural and Cognve Scence, Germany, 25. [16]Camazne, S. e al., Self-Organsaon n Bologcal Sysems. Prnceon Unversy Press, USA, 21. [17]Agular, J. Adapve Random Fuzzy Cognve Maps. Lecure Noes n Compuer Scence, Sprnger-Verlag, Vol. 2527, 22, pp [18]Moussaïd M., Helbng D., e al. Expermenal sudy of he behavoural mechansms underlyng self-organzaon n human crowds. Proceedngs of he Royal Socey B: Bologcal Scences, 29, 276: [19]Ball, P. Flow: Naure's Paerns: A Tapesry n Three Pars. Oxford Unversy Press, 29. [2]Perozo, N., Agular, J., Terán, O. Un Modelo Afecvo para una Arquecura Mulagene para Ssemas Emergenes y Auo-Organzados (MASOES), Submed for Publcaon o Revsa Técnca de la Faculad de Ingenería, Unversdad del Zula, Venezuela, 21. ISBN: